1
An Intuitive Guide to Linear Algebra (2012)
Despite two linear algebra classes, my knowledge consisted of "Matrices, determinants, eigen something something". Why? Well, let's try this course format:
Kalid Azad
BetterExplained teaches math the intuitive way: clear, visual lessons on imaginary numbers, exponents, calculus, trigonometry and more, with an Aha! moment before the details.
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Visit betterexplained.com → RSS feedOn Hacker News Jul 2009 – Apr 2022
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2
Convolution Is Fancy Multiplication
Like making engineering students squirm? Have them explain convolution and (if you're barbarous) the convolution theorem. They'll mutter something about…
3
What to know about the stock market (2007)
Everyone’s heard of the stock market — but few know why it works. Were you aware that each stock has two prices? That you can’t buy and sell for the same…
4
The Rule of 72 (2007)
The Rule of 72 is a great mental math shortcut to estimate the effect of any growth rate, from quick financial calculations to population estimates. Here’s…
5
An Interactive Guide to the Fourier Transform (2012)
The Fourier Transform is one of the deepest insights ever made. Unfortunately, the meaning is buried within dense equations:
6
A Programmer’s Intuition for Matrix Multiplication
What does matrix multiplication mean? Here's a few common intuitions: This is useful when first learning about vectors: vectors go in, new ones come out.…
7
Learn difficult concepts with the ADEPT method (2014)
After a decade of writing explanations, I've simplified the strategy I use to get new concepts to click. Here's how to teach yourself a difficult idea, or…
8
Intuitive Understanding of Euler’s Formula
Euler's identity seems baffling: It emerges from a more general formula: Yowza -- we're relating an imaginary exponent to sine and cosine! And somehow…
9
Aha Moments When Learning Git
Git is a fast, flexible but challenging distributed version control system. Before jumping in: Along with a book, tutorial and cheatsheet, here are the…
10
Life Lessons After 10 Years of BetterExplained.com
In 2006, a new entry popped into my idea journal: take my college notes and put them on a learning site. What should I call it: My name? Stuff explained…
11
Math and Analogies
Here's a talk on "Math And Analogies" I did for the Center on Contemporary Art (CoCA) in Seattle. What's this? Well, it's a number. Probably written down a…
12
Learning math? Think like a cartoonist
What's the essential skill of a cartoonist? Drawing ability? Humor? A deep well of childhood trauma? I'd say it's an eye for simplification, capturing the…
13
Complex numbers have never been so intuitive to me
Imaginary numbers always confused me. Like understanding e, most explanations fell into one of two categories: Gee, what a great way to encourage math in…
14
The Math Inside the US Highway System
At first glance, the US highway seems like a jumble of roads: However, the numbers follow a grid, with rules nobody told me (image source, click to enlarge):
15
Quake's Fast Inverse Square Root
I'm no graphics expert, but appreciate why square roots are useful. The Pythagorean theorem computes distance between points, and dividing by distance helps…
16
Avoiding the Adjective Fallacy
You're reading this, so I'll assume your English is pretty good. What's wrong with these phrases? Do you have a logical reason for why they sound strange? Or…
17
Finding Unity in the Math Wars
I usually avoid current events, but recent skirmishes in the math world prompted me to chime in. To recap, there've been heated discussions about math…
18
Colorized Math Equations
Years ago, while working on an explanation of the Fourier Transform, I found this diagram: Most ideas aren't inherently confusing, but their technical…
19
A Calculus Analogy: Integrals as Multiplication
Integrals are often described as finding the area under a curve. This description is too narrow: it's like saying multiplication exists to find the area of…
20
An Intuitive (and Short) Explanation of Bayes’ Theorem
Bayes’ theorem was the subject of a detailed article. The essay is good, but over 15,000 words long — here’s the condensed version for Bayesian newcomers like…